Saving Matricies from a Loop

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Kyle Fertig
Kyle Fertig 2017-12-4
回答： Mukul Rao 2017-12-6
I'm creating a function to create an inverse matrix of some [A] following LU Factorization, and I have the correct loops to generate the columns of the inverse (defined by p), but the loop happens "n" times where n is the number of rows/columns in the square matrix. The problem is that "p" is overwritten each time the loop goes through, and I need to save the values from each time the loop happens so I can eventually piece the rows together into a final matrix: inverse A. I did some research and came across cells, but I was unsuccessful trying to implement it into my own code shown below. Any help is appreciated!
Thanks,
-Kyle
%%Taking Apart Identity Matrix
L=[1,0,0;2.56,1,0;5.76,3.5,1]
U=[25,5,1;0,-4.8,-1.56;0,0,0.7]
w=length(L)
I=eye(w)
b=[1;0;0]
n=length(L)
for i=1:w
b=I(:,i)
%%Gauss Elim L
n=length(L);
m=zeros(n,1);
x=zeros(n,1);
for k =1:n-1;
%compute the kth column of M
m(k+1:n) = L(k+1:n,k)/L(k,k);
%compute
%An=Mn*An-1;
%bn=Mn*bn-1;
for i=k+1:n
L(i, k+1:n) = L(i,k+1:n)-m(i)*L(k,k+1:n);
end;
b(k+1:n)=b(k+1:n)-b(k)*m(k+1:n);
end
W= triu(L);
%BACKWARD ELIMINATION
x(n)=b(n)/L(n,n);
for k =n-1:-1:1;
b(1:k)=b(1:k)-x(k+1)* W(1:k,k+1);
x(k)=b(k)/W(k,k)
end
%%Gauss Elim U
n=length(U);
m=zeros(n,1);
p=zeros(n,1);
for k =1:n-1;
%compute the kth column of M
m(k+1:n) = U(k+1:n,k)/U(k,k);
%compute
%An=Mn*An-1;
%bn=Mn*bn-1;
for i=k+1:n
U(i, k+1:n) = U(i,k+1:n)-m(i)*U(k,k+1:n);
end;
x(k+1:n)=x(k+1:n)-x(k)*m(k+1:n);
end
W= triu(U);
%BACKWARD ELIMINATION
p(n)=x(n)/U(n,n);
for k =n-1:-1:1;
x(1:k)=x(1:k)-p(k+1)* W(1:k,k+1);
p(k)=x(k)/W(k,k)
end
end

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回答（1 个）

Mukul Rao
Mukul Rao 2017-12-6
Hello, I made some minor changes. Note that you had reused "i" as a loop-variable inside a nested for-loop, I renamed these to "j" to not corrupt the value of "i" in the outermost loop. Finally, initializing p to a square matrix of zeros and replacing all p(k) s with p(k,i)s does the trick.
%%Taking Apart Identity Matrix
L=[1,0,0;2.56,1,0;5.76,3.5,1]
U=[25,5,1;0,-4.8,-1.56;0,0,0.7]
w=length(L)
I=eye(w)
b=[1;0;0]
n=length(L)
p = zeros(w,w);
for i=1:w
b=I(:,i)
%%Gauss Elim L
n=length(L);
m=zeros(n,1);
x=zeros(n,1);
for k =1:n-1;
%compute the kth column of M
m(k+1:n) = L(k+1:n,k)/L(k,k);
%compute
%An=Mn*An-1;
%bn=Mn*bn-1;
for j=k+1:n
L(j, k+1:n) = L(j,k+1:n)-m(j)*L(k,k+1:n);
end;
b(k+1:n)=b(k+1:n)-b(k)*m(k+1:n);
end
W= triu(L);
%BACKWARD ELIMINATION
x(n)=b(n)/L(n,n);
for k =n-1:-1:1;
b(1:k)=b(1:k)-x(k+1)* W(1:k,k+1);
x(k)=b(k)/W(k,k)
end
%%Gauss Elim U
n=length(U);
m=zeros(n,1);
for k =1:n-1;
%compute the kth column of M
m(k+1:n) = U(k+1:n,k)/U(k,k);
%compute
%An=Mn*An-1;
%bn=Mn*bn-1;
for j=k+1:n
U(j, k+1:n) = U(j,k+1:n)-m(j)*U(k,k+1:n);
end;
x(k+1:n)=x(k+1:n)-x(k)*m(k+1:n);
end
W= triu(U);
%BACKWARD ELIMINATION
p(n,i)=x(n)/U(n,n);
for k =n-1:-1:1
x(1:k)=x(1:k)-p(k+1,i)* W(1:k,k+1);
p(k,i)=x(k)/W(k,k);
end
end
>> p
p =
0.0476 -0.0833 0.0357
-0.9524 1.4167 -0.4643
4.5714 -5.0000 1.4286
>> (L*U)*p
ans =
1.0000 0 0
0.0000 1.0000 0.0000
0.0000 -0.0000 1.0000

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